November 2025 (9709/12). Question 7

The coordinates of the points P and Q are (1,1) and (7,11) respectively. The line segment PQ forms a diameter of a circle.

(a) Find the equation of the circle. [4 marks]

(b) Find the equation of the tangent to the circle at the point Q. [3 marks]

(c) The other point on the circle with x-coordinate 7 is R. Find the coordinates of the point of intersection of the tangent at Q with the tangent at R. [4 marks].

9709/11/M/J/25q8 – Mark Scheme

The circle with equation x² + y² – 6x +10y – 27 = 0 intersects the line x = -2 at the points P and Q. Find the area of the triangle formed by the tangents to the circle at P and Q, and the line x = -2. [8 marks]